Báo cáo khoa học: "Quantifier Scope and Constituency" pot

Quantifier Scope and Constituency
Jong C. Park
Computer and Information Science
University of Pennsylvania
200 South 33rd Street, Philadelphia, PA 19104-6389, USA
park@line, cis. upenn, edu
Abstract
Traditional approaches to quantifier scope
typically need stipulation to exclude rea-
dings that are unavailable to human under-
standers. This paper shows that quantifier
scope phenomena can be precisely charac-
terized by a semantic representation cons-
trained by surhce constituency, if the di-
stinction between referential and quantifi-
cational NPs is properly observed. A CCG
implementation is described and compared
to other approaches.
1 Introduction
It is generally assumed that sentences with multi-
ple quantified NPs are to be interpreted by one or
more unambiguous logical forms in which the scope
of traditional logical quantifiers determines the rea-
ding or readings. There are two problems with this
assumption: (a) without further stipulation there is
a tendency to allow too many readings and (b) there
is considerable confusion as to how many readings
should be allowed arising from contamination of the
semantics of many NL quantifiers by referentiality.
There are two well-known techniques for redis-
tributing quantifiers in quantification structures:

quantifying-in (Montague, 1974; Cooper, 1983; Kel-
ler, 1988; Carpenter, 1994) and quantifier raising
(May, 1985). The former provides a compositio-
nal way of putting possibly embedded quantifiers
to the scope-taking positions, and the latter utili-
zes a syntactic movement operation at the level of
semantics for quantifier placement. There are also
approaches that put more emphasis on utilizing con-
textual information in restricting the generation of
semantic forms by choosing a scope-neutral repre-
sentation augmented with ordering constraints to
capture linguistic judgments (Webber, 1979; Kamp,
1981; Helm, 1983; Poesio, 1991; Reyle, 1993). And
there are computational approaches that screen una-
vailable and/or redundant semantic forms (Hobbs
Shieber, 1987; Moran, 1988; Vestre, 1991). This pa-
per will show that these approaches allow unavaila-
ble readings, and thereby miss an important gene-
ralization concerning the readings that actually are
available.
This paper examines English constructions that
allow multiple occurrences of quantified NPs: NP
modifications, transitive or ditransitive verbs, that
complements, and coordinate structures. Based on
a critical analysis of readings that are available from
these data, the claim is that scope phenomena can
be characterized by a combination of syntactic sur-
face adjacency and semantic function-argument re-
lationship. This characterization will draw upon the
old distinction between referential and quantificatio-

nal NP-semantics (Fodor & Sag, 1982). We choose
to use Combinatory Categorial Grammar to show
how surface adjacency affects semantic function-
argument relationship, since CCG has the flexibility
of composing almost any pair of adjacent constitu-
ents with a precise notion of syntactic grammatica-
lity (Steedman, 1990; 1993). z
The rest of the paper is organized as follows. First,
we discuss in §2 how traditional techniques address
availability of readings and note some residual pro-
blems. Then we give a brief analysis of available
readings (§3), a generalization of the analysis (§4),
and finally describe a computational implementation
in Prolog (~5).
2 Traditional Approaches
All three paradigms of grammar formalisms intro-
duced earlier share similar linguistic judgments for
their grammaticality analyses. This section exami-
nes quantifying-in to show (a) that quantifying-
in is a powerful device that allows referential NP-
interpretations and (b) that quantifying-in is not suf-
ficiently restricted to account for the available rea-
dings for quantificational NP-interpretations.
Quantifying-in is a technique originally introdu-
ced to produce appropriate semantic forms for de
re interpretations of NPs inside opaque operators
1 For instance, the result would transfer to Synchro-
nous "I~ee Adjoining Grammar (Shieber & Schabes,
1990) without much change.
205

(Montague, 1974). For example, (a) below has two
readings,
de re
and
de dicto,
depending on the rela-
tivity of the existence of such an individual. They
are roughly interpretable as (b) and (@2
(1) (a) John believes that a Republican will win.
(b) 3r.repub(r) A bel(john, uill(uin(r)))
(C) bel(john, 3r.repub(r) A
uill(uin(r)))
(b) has a binder 3 that is
quaati.fving
a variable r
inside an opaque operator bel, hence the name for
the technique. (c) does not have such an interven-
ing operator. Although it is beyond the scope of the
present paper to discuss further details of intensio-
nality, it is clear that
de re
interpretations of NPs
are strongly related to referential NP-semantics, in
the sense that the
de re
reading of (a) is about a
referred individual and not about an arbitrary such
individual. Quantifying-in is designed to make
any
(possibly embedded) NP take the matrix scope, by

leaving a scoped variable in the argument position
of the original NP. This would be acceptable for re-
ferential NP-semantics.
Montague also proposed to capture purely exten-
sional scope ambiguities using quantifying-in. For
example, wide scope reading of
a woman
in (a) below
is accounted for by quantifying-in (with a meaning
postulate), patterned after one for (b).
(2) (a) Every man loves a woman.
(b) Every man seeks a white unicorn.
His suggestion is adopted with various subsequent
revisions cited earlier. Since any NP, referential or
quantificational, requires quantifying-in to outscope
another, quantifying-in consequently confounds re-
ferential and quantificational NP-semantics. This
causes a problem when there is a distributional dif-
ference between referential NPs and non-referential
NPs, as Fodor & Sag (1982) have argued, a view
which has been followed by the approaches to dy-
namic interpretation of indefinite NPs cited earlier.
It seems hard to reconcile quantifying-in with these
observations.
3 Availability of Readings
This section proposes a way of sharpening our intui-
tion on available readings and re-examines traditio-
nal linguistic judgments on grammatical readings.
While there are undoubted differences in degree
of availability among readings dependent upon se-

mantics or discourse preference (Bunt, 1985; Moran,
1988), we will focus on all-or-none structural possi-
bilities afforded by competence grammar. 3
2In this simplistic notation, we gloss over tense ana-
lysis, among others.
3Moran's preference-based algorithm treats certain
readings as "highly unpreferred," effectively making
them structurally unavailable, from those possible sco-
Consider the following unambiguous quantifica-
tion structure in a generalized quantifier format
(hereafter oq, Barwise & Cooper, 1981), where
quantifier
outscopes
any quantifiers that may oc-
cur in either restriction or body.
(3) quantifier(variable, restriction, body)
Logical forms as notated this way make explicit the
functional dependency between the denotations of
two ordered quantificational NPs. For example~ con-
sider (4) (a) (Partee, 1975). (b) shows one way of
representing it in a GQ format.
(4) (a) Three Frenchmen visited five Russians.
(b) three(f, frenchmen(f), five(r,
russians (r), visited(f, r) ) )
We can always argue, by enriching the notation, that
(4) (b) represents at least four different readings, de-
pending on the particular sense of each involved NP,
i.e., group- vs individual-denoting. In every such
reading, however, the truth of (4) (b) depends upon
finding appropriate individuals (or the group) for f

such that
each
of those individuals (or the group
itself) gets associated with appropriate individuals
(or a group of individuals) for r via the relation
visil;ed. 4 Notice that there is always a
functional
dependency
of individuals denoted by r upon indi-
viduals denoted by f. We claim that this explicit
functional dependency can be utilized to test availa-
bility of readings. 5
First, consider the following sentences without
coordination.
(5) (a) Two representatives of three companies
saw most samples.
(b) Every dealer shows most customers at
most three cars.
(c) Most boys think that every man danced
with two women.
(a) has three quantifiers, and there are 6 different
ways of ordering them. Hobbs & Shieber (1987)
show that among these, the reading in which
two re-
presentatives
outscopes
most samples
which in turn
outscopes
three companies

is not available from the
sentence. They attribute the reason to the logical
structure of English as in (3), as it is considered
unable to afford an unbound variable, a constraint
known as the unbound variable constraint (uvc). 6
We should note, however, that there is one reading
pings generated by a scheme similar to Hobbs & Shieber
(1887). We clash that competence grammax makes even
fewer readings available in the first place.
4Without losing generality, therefore, we will consider
only individual-denoting NPs in this paper.
SSingular NPs such
as a company are
not helpful to
this task since their denotations do not involve multi-
ple individuals which explicitly induce this functional
dependency.
eThe reading would be represented as follows, which
has the first occurrence of the variable c left unbound.
206
among the remaining five that the uvc allows which
in fact does not appear to be available. This is the
one in which
three companies
outscopes
most samp-
les
which in turn outscopes two
representatives
(cf.

Horn (1972), Fodor (1982)). 7 This suggests that
the uvc may not be the only principle under which
Hobbs & Shieber's reading is excluded, s The other
four readings of (a) are self-evidently available. If
we generalize over available readings, they are only
those that have no quantifiers which intercalate over
NP boundaries. 9
(5) (b) has three quantifiers too, but unlike (5)
(a), all the six ways of ordering the quantifiers are
available. (5) (c) has only four available readings,
where
most boys
does not intercalate
every man
and
two women. 1°
Consider now sentences including coordination.
(6) (a) Every girl admired, but most boys dete-
sted, one of the saxophonists.
(b) Most boys think that every man danced
with, but doubt that a few boys talked to,
more than two women.
As Geach (1970) pointed out, (a) has only two gram-
matical readings, though it has three quantifiers. In
reading 1, the same saxophonist was admired and
detested at the same time. In reading 2, every girl
admired an arbitrary saxophonist and most boys
also detested an arbitrary saxophonist. In particu-
lar, missing readings include the one in which every
girl admired the same saxophonist and most boys

detested the same but another saxophonist. (6) (b)
rio(r,
rep(r) It
of(r,c),
most(a,
samp(s),
three(c, comp(c), sag(r,s))))
7To paraphrase this impossible reading, it is true of a
situation under which there were three companies such
that there were four samples for each such company such
that each such sample was seen by two representatives of
that company. Crucially, samples seen by representatives
of different companies were not necessarily the same.
SThis should not be taken as denying the reality of the
uvc itself. For example, as one of the referees pointed
out, the uvc is required to explain why, in (a) below,
every professor
must outscope
a friend
so as to bind the
pronoun
his.
(a) Most students talked to a friend of every pro-
fessor about his work.
9One can replace
most samples
with other complex
NP such as
most samples of at least five products
to see

this. Certain sentences that apparently escape this ge-
nerafization will be discussed in the next section.
1°To see why they are available, it is enough to see
that (a) and (b) below have two readings each.
(a) 3ohn thinks that every man danced with two
women.
(b)
Most boys think
that
Bill danced with two
women.
also has only two grammatical readings. In one,
most boys
outscopes every
man
and
a few boys
which
together outscope
more than two women.
In the
other,
more than two women
outscopes every
man
and
a few boys,
which together outscope
most boys.
4 An Account of Availability

This section proposes a generalization at the level of
semantics for the phenomena described earlier and
considers its apparent counterexamples.
Consider a language £ for natural language se-
mantics that explicitly represents function-argument
relationships (Jackendoff, 1972). Suppose that in £:
the semantic form of a quantified NP is a syntactic
argument of the semantic form of a verb or a pre-
position. (7) through (10) below show well-formed
expressions in £.11
(7)
visitld(five(rulsiim) ,thrse(frencluiin))
(8)
saw(most (sanp) ,of (thres(cmap) ,two(rap)))
(9)
show (three(car) ,most (cstmr), every(dlr))
(10) think(Adlmced(two(woman)
,every(nan)),
most (boy))
For instance, of has two arguments
three(comp)
and two(rep), and show has three arguments.
/: gives rise to a natural generalization of available
readings as summarized below. 12
(11) For a function with n arguments, there are
n! ways of successively providing all the ar-
guments to the function.
This generalization captures the earlier observations
about availability of readings. (7), for (4) (a), has
two (2!) readings, as viaited has two arguments.

(8) is an abstraction for four (2!x2!) readings, as
both of and maw have two arguments each. (9) is an
abstraction for six (3!) readings, as show has three
arguments. Likewise, (10) is an abstraction for four
readings.
Coordination gives an interesting constraint on
availability of readings. Geach's observation that
(6) (a) has two readings suggests that the scope of
the object must be determined
before
it reduces with
the coordinate fragment. Suppose that the non-
standard constituent for one of the conjuncts in (6)
(a) has a semantic representation shown below.
(12)
~z adnired(z,svery(girl))
Geach's observation implies that (12) is ambiguous,
so that every(girl) can still take wide (or narrow)
scope with respect to the unknown argument. A
11The up-operator ^ in (10) takes a term of type t to
a term of type e, but a further description of £ is not
relevant to the present discussion.
12Nan (1991)'s work is based on a related observation,
though he does not make use of the distinction between
referential and quantificational NP-semantics.
207
theory of CCG will be described in the next sec-
tion to show how to derive scoped logical forms for
available readings only.
But first we must consider some apparent coun-

terexamples to the generalization,
(13) (a) Three hunters shot at five tigers.
(b) Every representative of a company saw
most samples.
The obvious reading for (a) is called conjunctive or
cumulative (Partee, 1975; Webber 1979). In this
reading, there are three hunters and five tigers such
that shooting events happened between the two par-
ties. Here, arguments are not presented
in succes-
sion
to their function, contrary to the present gene-
ralization. Notice, however, that the reading must
have two (or more) referential NPs (Higginbotham,
1987). 13 The question is whether our theory should
predict this possibility as well. For a precise notion
of availability, we claim that we must appeal to the
distinction between referential and quantificational
NP-semantics, since almost any referential NP can
have the appearance of taking the matrix scope, wi-
thout affecting the rest of scope phenomena. A re-
lated example is (b), where in one reading a referen-
tial NP
a company
arguably outscopes
most samples
which in turn outscopes every
representative
(Hobbs
& Shieber, 1987). As we have pointed out earlier,

the reading does not generalize to quantified NPs in
general.
(14)
(a) Some student will investigate two dia-
lects of every language.
(b) Some student will investigate two dia-
lects of, and collect all interesting examp-
les of coordination in, every language.
(c) * Two representative of at least three
companies touched, but of few universi-
ties saw, most samples.
(a) has a reading in which
every language
outscopes
some student
which in turn outscopes
two dialects
(May, 1985). In a sense, this has intercalating NP
quantifiers, an apparent problem to our generaliza-
tion. However, the grammaticality of (b) opens up
the possibility that the two conjuncts can be repre-
sented grammatically as functions of arity two, si-
milar to normal transitive verbs. Notice that the
generalization is not at work for the fragment
of at
least three companies touched
in (c), since the con-
junct is syntactically ungrammatical. At the end of
next section, we show how these finer distinctions
are made under the CCG framework (See discussion

of Figure 5).
IZFor
example, (a) below lacks such a reading.
(a) Several men danced with few women.
5 A CCG Implementation
This section describes a CCG approach to deriving
scoped logical forms so that they range over only
grammatical readings.
We will not discuss details of how CCG charac-
terizes natural language syntactically, and refer the
interested reader to Steedman (1993). CCGs make
use of a limited set of combinators, type raising (T),
function composition (B), and function substitution
(S), with directionality of combination for syntac-
tic grammaticality. For the examples in this pa-
per, we only need type raising and function composi-
tion, along with function application. The following
shows rules of derivation that we use. Each rule is
associated with a label, such as > or <B etc, shown
at the end.
(15) (a) x/v ~ => x
(>)
(b)
Y
x\~ => x (<)
(c) x/v Y/Z => x/z (>a)
(d) Y\z
x\Y
ffi> x\z (<e)
(e) np => T/(T\np) (>T)

(f) np => T\(T/np) (<T)
The mapping from syntax to semantics is usually
defined in two different ways. One is to use ele-
mentary categories, such as np or s, in encoding
both syntactic types and logical forms (Jowsey, 1990;
Steedman, 1990; Park, 1992). The other is to asso-
ciate the entire lexical category with a higher-order
expression (Kulick, 1995). In this paper, we take the
former alternative to describe a first-order rendering
of CCG.
Some lexical entries for
every
are shown below.
(16)
(s :q-every (X, N, S)/(s : S\np:I) )/n:X'N
(17)
(s : S/(a : Sknp: s-every(1) ) )/n:W
The information (s/(s\np))/n encodes the syntac-
tic fact that
every
is a constituent which, when
a constituent of category n is provided on its
right, returns a constituent of category s/(s\np).
q-every(X,li,S) is a term for scoped logical forms.
We are using different lexical items, for instance
q-every and e-every
for
every,
in order to signify
their semantic differences. 14 These lexical entries

are just two instances of a general schema for type-
raised categories of quantifiers shown below, where
T is an arbitrary category.
(18) (T/(T\np))/na~d (T\(T/np))/n
And the semantic part of (16) and (17) is first-order
encoding of (19) (a) and (b), respectively. 15
14q-every
represents
every
as a quantifier, and
s-every, as a set denoting property. We will
use s-every(l^man(X)) and its ~-reduced equivalent
s-every(man) interchangeably.
1as-quantifier(noun) denotes an arbitrary set N of
individuals d such that d has the property noun and that
the cardinality of N is determined by quantifier (and
208
(19) (a) ~n.AP.Vz E s-every(n).P(=)
(b)
(a) encodes wide scope type raising and (b), narrow.
With standard entries for verbs as in (20), logical
forms such as (21) and (22) are po ible.
(20) saw :- (s:sav(I,Y)\np:X)/np:¥
(21) q-two (X, rep (X), aaw(X, s-f ottr (samp)) )
(22) q-two(X,rep(X) ,q-four(Y,samp(Y),aaw(][,¥)))
Figure 1 shows different ways of deriving
scoped logical forms. In (a), n:I'!
unifies
with
n:X'girl(X), so that Ii gets the value girl(X).

This value of !1 is transferred to the expression
s:evory(X,li,S) by partial execution (Pereira
Shieber, 1987; Steedman, 1990; Park, 1992). (a)
shows a derivation for a reading in which object NP
takes wide scope and (b) shows a derivation for a rea-
ding in which subject NP takes wide scope. There
are also other derivations.
Figure 2 shows logical forms that can be derived in
the present framework from Geach's sentence. No-
tice that the conjunction forces subject NP to be first
composed with the verb, so that subject NP must be
type-raised
and
be combined with the semantics of
the transitive verb. As noted earlier, the two catego-
ries for the object still make both scope possibilities
available, as desired. The following category is used
for
but.
(23)
((s : and(P ,1~)/np:][)\ (s:P/np:][))/(s :Q/np :][)
Readings that involve intercalating quantifiers, such
as the one where every
girl
outscopes
one sazopho-
nist,
which in turn outscopes
most bogs,
are correctly

excluded.
Figure 3 shows two different derivations of logi-
cal forms for the complex NP
two representatives of
three companies.
(a) shows a derivation for a rea-
ding in which the modifying NP takes wide scope
and (b) shows the other case. In combination with
derivations involving transitive verbs with subject
and object NPs, such as ones in Figure 1, this cor-
rectly accounts for four grammatical readings for (5)
(a). 16
Figure 4 shows a derivation for a reading, among
six, in which
most customers
outscopes every
dealer
which in turn outscopes
three cars.
Some of these
readings become unavailable when the sentence con-
tains coordinate structure, such as one below.
(24) Every dealer shows most customers (at most)
three cars but most mechanics every car.
noun). We conjecture that this can also be made to cap-
ture several related NP-semantics, such as collective NP-
semantics and/or referential NP-semantics, though we
can not discuss further details here.
lSAs we can see in Figure 3 (a) (b), there m no
way quantifiers inside $ can be placed

between
the two
quantifiers two & three, correctly excluding the other
two readings.
In particular, (24) does not have those two readings
in which every
dealer
intercalates
most customers
and
three cars.
This is exactly predicted by the pre-
sent CCG framework, extending Geach's observa-
tion regarding (6) (a), since the coordination forces
the two NPs,
most customers
and
three cars,
to be
composed first (Dowty, 1988; Steedman 1990; Park
1992). (25) through (27) show one such derivation,
which results in readings where
three cars
outscopes
most customers
but every
dealer
must take either
wide or narrow scope with respect to both
most cu-

stomers
and
three cars.
(25) -oat cuato.ers
(26)
(2T)
((s:q-most(Z,catm'(g),S)~p:g)/np:Y)
\(((s:S\np:X)/np:T)/np:Z)
three cars
(e:q-three(Y,car(Y),S)\np:l)
\((s:$\np:X)/n]p:f)
ao|t custoaera
three
cars
see above see above
<B
(s:q-three(¥,car(Y),q-ttost(Z,catmr(Z),S))
\np:X)\(((e:S\np:X)/np:T)/np:g)
Figure 5 shows the relevant derivation for the frag-
ment
investigate two dialects of
discussed at end of
previous section. It is a conjoinable constituent, but
since there is no way of using type-raised category
for two for a successful derivation, two
dialects can
not outscope any other NPs, such as subject NP or
the modifying NP (Steedman, 1992). This correctly
accounts for our intuition that (14) (a) has an ap-
parently intercalating reading and that (14) (b) has

only two readings. However, there is no similar deri-
vation for the fragment
of three companies touched,
as shown below.
(28) of three
companies touched
(n\n)/np T\(T/np) (e\np)/np
<
n\n (with T =' n\n)
6 Concluding Remarks
We have shown that the range of grammatical rea-
dings allowed by sentences with multiple quantified
NPs can be characterized by abstraction at function-
argument structure constrained by syntactic adja-
cency. This result is in principle available to other
paradigms that invoke operations like QR at LF or
type-lifting, which are essentially equivalent to ab-
straction. The advantage of CCG's very free notion
209
(a)
every
girl
admired one saxophonist
s:q-every(X,l.S) n:X'girl(X) (s:adaired(X.Y)~np:X) s:q-one(Y,sax(Y),S)\(s:S/np:Y)
/(s:S\np:X)/n:X'i /np:¥
s:q-every(X,girl(X),S)/(s:S\np:X)
>B
=:q-every(X.girl(X).adaired(X,Y))/np:Y
(b)
s:q-one(Y,sax(Y).q-every(X,girl(X,adaired(X.Y))))

every girl admired
s:q-every(X.girl(X).S)/(s:S\np:X) (s:adaired(X.Y)~np:l)
/np:Y
s:q-every(X,girl(X).adaired(X,Y))/np:Y
one saxophonist
s:S\(s:S/np:s-one(sax))
s:q-every(X.girl(X).adaired(X.s-one(sax)))
Figure 1: Every girl admired one sazophonist: Two sample derivations
(a)
every
girl
admired
but most boys detested one saxophonist
s:q-every(X,girl(l).adaired(l.Y))/np:Y > s:S\(s:S/np:s-one(sax))
<
s:and(q-every(X,girl(1),~l~-~l(l,Y)),q-most(l,boy(1),detested(X,Y)))/np:Y
(b)
•:and(q-every(x••irl(•)•ad•ired(••s-•ne(•ax)))•q-•••t(X•b•y(X)•detested(••s-•ne(sax))))
every girl admired but most boys detested one saxophonist
s:adaired(s-every(girl),Y)/np:Y ~ s:q-one(Y,sax(Y),S)\(s:S/np:¥)
s:and(admired(s-every(girl),Y),detested(s-most(boy),W))/np:Y
s:q-one(Y,sax(Y),and(adaired(s-every(girl),Y),detested(s-most(boy),Y)))
Figure 2:
Every girl admire~ but most boys detested, one sazophonist:
Two sample derivations
(a)
two representatives of three companies
(s:q-teo(X.|.S)
/(s:S~np:l))/n:l'l
n:X'and(rep(X),of(X.Y))/np:Y

>B
.(s:q-tvo(l,and(rep(l),of(X,Y)),S)/(s:S\np:X))/np:¥
(s:q-three(C.comp(C),S2)/(s:St\np:l))
\((s:S2/(s:Sl~np:l))/np:C)
(b)
a:q-three(C,comp(C).q-two(X.and(rep(X),of(X.C)),S))/(s:S\np:X)
two representatives of three companies
(s:q-twoCX,l,s) n:X'and(rep(i).of(X,Y))/np:Y (s:S2/(s:St\np:X))
/(s:S\np:i))/n:g'N \((s:S2/(s:St\np:X))/np:s-three(coap))
>B
(s:q-two(X.and(rep(X),of(X,Y)),S)/(s:S\np:X))/np:Y
s :q-tgo (X, and(rep(l) ,of (X,s-three (¢oap)))
,S)/(s:S\np:I)
Figure 3:
two representatives o/three companies:
Two sample derivations
210
every dealer shows host custoners
s:q-every(X,dlr(X),S) (s:ehow(X,Y,g)\np:I) (s:q-nost(Y,cstnr(Y),S)
/(s:S\np:l) /np:g/np:Y /np:g)\(s:S/np:g)/np:Y

>B
s:q-every(X,dlr(X),shog(X,Y,g)/np:Z/np:Y
s:q-nost(Y,cstaw(Y),q-every(X,dlr(X),show(X,Y,Z)))/np:g
three cars
s:S\(s:S
/np:s-three(car))
s:q-nost(Y,cstnr(Y),q-every(X,dlr(X),show(X,Y,s-three(car))))
Figure 4:
Every dealer shows most customers three cars:

One sample derivation
investigate
two dialects of
(s:investigate(X,g)~ap:X)
/np:Y
np:s-two(l) n:lt/(n:il (n:Y'tnd(l,of(l,Z))~n:I1)
/n:i \n:Y'dialect(Y))
/np:g
~B
n: Y'and(dialect (g) ,of (g,z))/np:Z

>B
rip:
s-two(Y'and(dialect (¥), of (Y,Z)))/rip: Z
~B
(s:investigate(g,s-tuo(Y'and(dialect(Y),of(Y,Z)))\np:X)/np:Z
Figure 5:
investigate two dialects of.
One derivation
of surface structure is that it ties abstraction or the
equivalent as closely as possible to derivation. Ap-
parent counterexamples to the generalization can be
explained by the well-known distinction between re-
ferential and quantificational NP-semantics. An im-
plementation of the theory for an English fragment
has been written in Prolog, simulating the 2nd order
properties.
There is a question of how the non-standard sur-
face structures of CCG are compatible with well-
known conditions on binding and control (including

crossover). These conditions are typically stated on
standard syntactic dominance relations, but these
relations are no longer uniquely derivable once CCG
allows non-standard surface structures. We can
show, however, that by making use of the obliquen-
ess hierarchy (of. Jackendoff (1972) and much sub-
sequent work) at the level of LF, rather than sur-
face structure, it is possible to state such conditions
(Steedman, 1993).
Acknowledgements
Special thanks to Mark Steedman. Thanks also to
Janet Fodor, Beryl Hoffman, Aravind Joshi, Nobo
Komagata, Anthony Kroch, Michael Niv, Charles L.
Ortiz, Jinah Park, Scott Prevost, Matthew Stone,
Bonnie Webber, and Michael White for their help
and criticism at various stages of the presented
idea. Thanks are also due to the anonymous referees
who made valuable suggestions to clarify the paper.
Standard disclaimers apply. The work is supported
in part by NSF grant nos. IRI91-17110, and CISE
IIP, CDA 88-22719, DARPA grant no. N660001-94-
C-6043, and ARO grant no. DAAH04-94-G0426.
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